1. Field of the Invention
This invention generally relates to acoustic waveguides and in particular to a method and system for modeling the design of an acoustic waveguide based upon predicted performance standards and performance metrics for a waveguide having certain physical characteristics and dimensions.
2. Related Art
Often times, loudspeakers consist of a transducer or driver unit coupled to a waveguide. A waveguide can also be commonly referred to as a horn or acoustic waveguide. A waveguide functions to provide gain for the transducer, i.e., increases the acoustic sensitivity of the loudspeaker in a region of frequencies. A waveguide can also assist in the control of dispersion on and off-axis as well as assist with directivity mating with other transducers and can simplify loudspeaker system integration.
Typical waveguides include a “throat” or entrance at one end and a “mouth” or exit at the opposing end. The throat end of the waveguide is typically coupled to the transducer or driver and receives the initial input of sound from the driver. The waveguide then usually increases in cross-sectional area or flares out as it approaches the mouth. The sound is then dispersed through the mouth, which is the exit of the waveguide. Thus, the throat end of the waveguide is typically narrower in cross-section in both the horizontal and vertical directions and generally defines a bounded region that directs the sound from the throat to the mouth of the waveguide. This interior bounded region may be referred to as the waveguide profile. The sound produced as planar surfaces parallel to the throat, are referred to as wave fronts.
In operation, the surfaces of the waveguide in a loudspeaker typically produce a coverage pattern of a specified total coverage angle that may differ horizontally and vertically. The coverage angle is a total angle in any plane of observations, although horizontal and vertical orthogonal planes are typically used. The coverage angle is evaluated as a function of frequency and is defined to be the angle at which the intensity of sound (Sound Pressure Level—SPL) is half of the SPL on the reference axis, which is the axis direction usually normal to the throat of the driver.
Acoustic energy radiates into the throat from the transducer at high pressure, with a wave front that is nominally flat and free of curvature. As the wave front expands outward to toward the mouth of the waveguide, the axial area increases in a uniform and monotonically increasing fashion. Analogous to electrical transformers in the electrical domain, waveguides can be considered as acoustical transformers in the acoustical domain. In the acoustical domain, waveguides contain impedance along the profile with resistive and reactive components. However, sound pressure level is produced primarily by the acoustical resistance of the waveguide. That is, acoustical reactance does not contribute to the sound pressure level. In the work presented, the rate of increasing area is controlled by an area expansion function designed to provide minimal acoustic reactance (or maximum acoustic radiation resistance at the throat). This approach increases the sensitivity and ultimately, the efficiency of the transducer and waveguide assembly.
The determined area expansion rate is intended to create a uniform dispersion pattern on and off-axis by manipulating the acoustical impedance as a function of frequency to theoretically lower frequency range of operation. The coupling of the waveguide acoustic impedance source to the acoustic impedance of the surrounding environment; provides an action analogous to an electrical transformer. The winding ratio is equivalent to the ratio of the radiation resistance seen by the driver and the radiation resistance of the surrounding environment. In this analogy, the change in pressure from the throat to the mouth of the waveguide is equivalent to the change in voltage across an electrical transformer.
The shape of an acoustic waveguide affects the frequency response, polar pattern and the level of harmonic distortion of sound waves as they propagate away from the acoustic waveguide. As loudspeakers produce sound waves, waveguides are used to control the characteristics of the acoustic wave propagation. As previously stated, the increase in area of the waveguide from throat to mouth is typically controlled by an area expansion function designed to provide appropriate acoustic impedance. Many different theories on waveguide design have been developed in the past to help determine the optimal expansion functions for waveguide designs.
One common design approach, developed by Keele, involves a two-section waveguide or horn design. In this design approach, an exponential design is used on the section near the throat, while the outer section utilizes a conical design approach. Similarly, Geddes developed an alternative design approach that is a well known in the industry. This approach uses exponential algebraic equations and functions developed by Geddes to determine the optimal contour of a waveguide once required values for the throat radius and coverage angle have been determined.
Current design approaches, such as those taught by Keele and Geddes, first determine the desired performance standards of the waveguide and then design the waveguide using established exponential functions or algebraic equations that are designed to model a waveguide to achieve the desired standards. No design method currently exists, however, that uses the performance standards of a waveguide of known contours and dimensions as a design metric. Additionally, no design method currently exists that captures the change in acoustic impedance, in particular the change in acoustic reactance, along the profile of the waveguide as part of the design standard. A need therefore exists for a waveguide design method such that one can predict the performance standards of waveguides having various contours and dimensions without the necessity of building a prototype. Under this proposed approach, design iterations can be made before the prototype stage of the waveguide since the performance standards may be predicted in advance of the design.